General, Organic, and Biological Chemistry
General, Organic, and Biological Chemistry
7th Edition
ISBN: 9781285853918
Author: H. Stephen Stoker
Publisher: Cengage Learning
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Textbook Question
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Chapter 2, Problem 2.51EP

Carry out the following additions and subtractions, expressing your answer to the correct number of significant figures. Assume that all numbers are measured numbers.

  1. a. 12 + 23 + 127
  2. b. 3.111 + 3.11 + 3.1
  3. c. 1237.6 + 23 + 0.12
  4. d. 43.65 – 23.7

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The answer for the given addition problem 12+23+127 must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.51EP

When the problem 12+23+127 is solved, the answer (162) is obtained.  But there are no inferred decimal points to say the significant figures.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, 12+23+127, the obtained answer is 162,  But in this problem there are no decimal points to determine the significant figure.

  12significantfigure=223significantfigure=2+127significantfigure=3162¯significantfigure=no digits to the right of the inferred decimal point

Conclusion

The answer obtained is 162, but there are no decimal points in the measurements in the problem to identify the significant figures.

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The answer for the given addition problem 3.111+3.11+3.1 must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.51EP

When the problem 3.111+3.11+3.1 is solved, the answer (9.3) is obtained with one significant figure to the right side of the decimal point.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, 3.111+3.11+3.1, 3.111 has three significant figures to the right side of the decimal point, whereas 3.11 and 3.1 has two significant figures and one significant figure to the right side of the decimal point respectively.  Hence the fewest significant figure here is one.

3.111significantfigure=33.11significantfigure=2+3.1significantfigure=19.3¯significantfigure=one digit to the right of the decimal point

Conclusion

The fewest significant figure in the measurements of the problem is one. The answer obtained is 9.3 with one significant figure.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The answer for the given addition problem 1237.6+23+0.12 must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.51EP

When the problem 1237.6+23+0.12 is solved, the answer (1261) is obtained.  But there are no inferred decimal points to say the significant figures.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, 1237.6+23+0.12, the obtained answer is 1261,  But in this problem there are no decimal points to determine the significant figures.

1237.6significantfigure=123significantfigure=nodecimalpoint+0.12significantfigure=21261¯significantfigure=no digits to the right of the inferred decimal point

Conclusion

The answer obtained is 1261, but there are no decimal points in the measurements in the problem to identify the significant figures.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The answer for the given subtraction problem 43.65-23.7 must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.51EP

When the problem 43.65-23.7 is solved, the answer (20.0) is obtained with one significant figure to the right side of the decimal point.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, 43.65-23.7, 43.65 has two significant figures to the right side of the decimal point, whereas 23.7 has one significant figure to the right side of the decimal point.  Hence the fewest significant figure here is one.

43.65significantfigure=223.7significantfigure=120.0¯significantfigure=one digit to the right of the inferred decimal point

Conclusion

The fewest significant figure in the measurements of the problem is one. The answer obtained is 20.0 with one significant figure.

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Chapter 2 Solutions

General, Organic, and Biological Chemistry

Ch. 2.3 - Prob. 2QQCh. 2.4 - Prob. 1QQCh. 2.4 - Prob. 2QQCh. 2.4 - Prob. 3QQCh. 2.4 - Prob. 4QQCh. 2.4 - Prob. 5QQCh. 2.4 - Prob. 6QQCh. 2.5 - In which of the following cases is the given...Ch. 2.5 - When rounded to three significant figures, the...Ch. 2.5 - Prob. 3QQCh. 2.5 - Prob. 4QQCh. 2.6 - Prob. 1QQCh. 2.6 - Prob. 2QQCh. 2.6 - Prob. 3QQCh. 2.6 - Prob. 4QQCh. 2.6 - Prob. 5QQCh. 2.6 - Prob. 6QQCh. 2.7 - Prob. 1QQCh. 2.7 - Prob. 2QQCh. 2.7 - Which of the following is an incorrect conversion...Ch. 2.7 - Prob. 4QQCh. 2.8 - Prob. 1QQCh. 2.8 - Prob. 2QQCh. 2.9 - Prob. 1QQCh. 2.9 - Prob. 2QQCh. 2.9 - Prob. 3QQCh. 2.9 - What is the mass, in grams, of 30.0 mL of liquid...Ch. 2.10 - The freezing point of water is a. 0F b. 0 K c. 0C...Ch. 2.10 - Prob. 2QQCh. 2.10 - Prob. 3QQCh. 2.10 - Prob. 4QQCh. 2 - What is the main reason scientists prefer to use...Ch. 2 - List the more common types of measurements made in...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Complete the following table by filling in the...Ch. 2 - 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Complete the following table by filling in the...Ch. 2 - Complete the following table by filling in the...Ch. 2 - Without actually solving, indicate the number of...Ch. 2 - Without actually solving, indicate the number of...Ch. 2 - Prob. 2.49EPCh. 2 - Carry out the following multiplications and...Ch. 2 - Carry out the following additions and...Ch. 2 - Carry out the following additions and...Ch. 2 - What is the uncertainty in the measured value...Ch. 2 - What is the uncertainty in the measured value...Ch. 2 - For each of the following numbers, will the...Ch. 2 - For each of the following numbers, will the...Ch. 2 - Prob. 2.57EPCh. 2 - Prob. 2.58EPCh. 2 - Prob. 2.59EPCh. 2 - For each of the numbers in Problem 2-56, how many...Ch. 2 - Express the following measured values in...Ch. 2 - Express the following measured values in...Ch. 2 - Change each of the following measured values from...Ch. 2 - Change each of the following measured values from...Ch. 2 - Prob. 2.65EPCh. 2 - Prob. 2.66EPCh. 2 - What is the uncertainty, in terms of a power of...Ch. 2 - What is the uncertainty, in terms of a power of...Ch. 2 - Write each of the following numbers in scientific...Ch. 2 - Write each of the following numbers in scientific...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Give the two forms of the conversion factor that...Ch. 2 - Prob. 2.75EPCh. 2 - Indicate whether each of the following equations...Ch. 2 - Using dimensional analysis, convert each of the...Ch. 2 - Using dimensional analysis, convert each of the...Ch. 2 - The human stomach produces approximately 2500 mL...Ch. 2 - A typical loss of water through sweating for a...Ch. 2 - The mass of premature babies is customarily...Ch. 2 - The smallest bone in the human body, which is in...Ch. 2 - What volume of water, in gallons, would be...Ch. 2 - What volume of gasoline, in milliliters, would be...Ch. 2 - An individual weighs 83.2 kg and is 1.92 m tall....Ch. 2 - An individual weighs 135 lb and is 5 ft 4 in....Ch. 2 - Prob. 2.87EPCh. 2 - Prob. 2.88EPCh. 2 - Prob. 2.89EPCh. 2 - When each of the following measurements of mass is...Ch. 2 - A sample of mercury is found to have a mass of...Ch. 2 - A sample of sand is found to have a mass of 12.0 g...Ch. 2 - Acetone, the solvent in nail polish remover, has a...Ch. 2 - Silver metal has a density of 10.40 g/cm3. What is...Ch. 2 - The density of homogenized milk is 1.03 g/mL. How...Ch. 2 - Nickel metal has a density of 8.90 g/cm3. How much...Ch. 2 - Water has a density of 1.0 g/cm3 at room...Ch. 2 - Air has a density of 1.29 g/L at room temperature....Ch. 2 - Prob. 2.99EPCh. 2 - A two-gram sample of a red-colored liquid is found...Ch. 2 - Calculate the volume, in milliliters, for each of...Ch. 2 - Calculate the volume, in milliliters, for each of...Ch. 2 - An oven for baking pizza operates at approximately...Ch. 2 - A comfortable temperature for bathtub water is...Ch. 2 - Mercury freezes at 38.9C. What is the coldest...Ch. 2 - Prob. 2.106EPCh. 2 - Prob. 2.107EPCh. 2 - Which is the higher temperature, 15C or 4F?
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